derivative of sin(3xln(sech(2x)))

Lösung

\frac{d}{d x} (sin (3 x) ln (sech (2 x)))

3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x)

Schritte zur Lösung

\frac{d}{d x} (sin (3 x) ln (sech (2 x)))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (3 x), g = ln (sech (2 x))

= \frac{d}{d x} (sin (3 x)) ln (sech (2 x)) + \frac{d}{d x} (ln (sech (2 x))) sin (3 x)

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

\frac{d}{d x} (ln (sech (2 x))) = - 2 tanh (2 x)

= cos (3 x) \cdot 3 ln (sech (2 x)) + (- 2 tanh (2 x)) sin (3 x)

Vereinfache

= 3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x)

\frac{\partial}{\partial y} (ln (x^{2} + y^{2} + 2))

n = 1 \sum \infty \frac{x ^{n}}{1 ^{n}}

\int (1 + x)^{3} d x

d er i v a t i v e f (x) = \frac{x ^{2} - 3 x + 4}{x + 2}

a re a 1 + x - x^{2} - x^{3}, 1 - x